I managed to create nice graphs saved to png (and svg or pdf). I have about 500 points for which I want to create this kind of graph. Now I wonder, if there is a way to take the minimum and maximum value of all these records to define the extend of my graph to make them comparable. E.g. each graph shows the temperature per depth but per point of measurement there is a difference in the temperature. In one point the temperature range might be 20-23 degrees, in another point 19-24. To make the graphs comparable it would be nice to have the option to define a minimum and maximum value that would be used for the definition of the axis.

Controlling the axes of the graph—Help | ArcGIS Desktop suggests you can control the axes range, but you would have to check to see if these values can persist between graphs. MatPlotlib provides a much more controlled environment for batch processing of graphs (it is builtin to current version of arcmap).